An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physics-informed machine learning and automated transformations of differential equations

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

The lightweight Base library for shared types and functionality for defining differential equation and scientific machine learning (SciML) problems

A Julia package to perform Bifurcation Analysis

Linear operators for discretizations of differential equations and scientific machine learning (SciML)

DeepONets, (Fourier) Neural Operators, Physics-Informed Neural Operators, and more in Julia

Automatic Finite Difference PDE solving with Julia SciML

Universal modeling and simulation of fluid mechanics upon machine learning. From the Boltzmann equation, heading towards multiscale and multiphysics flows.

Solve non-linear HJB equations.

ETH course - Solving PDEs in parallel on GPUs

A scientific machine learning (SciML) wrapper for the FEniCS Finite Element library in the Julia programming language

Meshless large eddy simulation through the reformulated vortex particle method

Solve Fractional Differential Equations using high performance numerical methods

A Julia package for Deep Backwards Stochastic Differential Equation (Deep BSDE) and Feynman-Kac methods to solve high-dimensional PDEs without the curse of dimensionality

Taylor-mode automatic differentiation for higher-order derivatives

Incompressible Navier-Stokes solver

CUDA acceleration for Trixi.jl

Sparse Grid Discretization with the Discontinuous Galerkin Method for solving PDEs

A simple finite volume tool for Julia

An array type for MPI halo data exchange in Julia